LOCAL LIMIT THEOREMS FOR FINITE AND INFINITE URN MODELS

By Hsien-Kuei Hwang, Svante Janson. 2006

61 citations recorded by the source corpus.

Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for normal approximation.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f2ba329fd272883e9df98859923b00ce79f81611

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws ∗ (2007, background): “Hwang and Janson [25] have shown a more delicate local CLT for Kn under V (t) → ∞.”
Stein couplings for normal approximation (2010, background): “The literature on this topic is rich; see for example Johnson and Kotz (1977), Kolchin, Sevast′yanov, and Chistyakov (1978) or Barbour, Holst, and Janson (1992), but also more recent results such as Hwang and Janson (2008) and Barbour (2009) on local limits theorems for infinite number of urns.”
Concentration inequalities in the infinite urn scheme for occupancy counts and the missing mass, with applications (2014, methodology): “For example the work of Hwang and Janson [2008] (eﬀectively) provides a local limit theorem for K n provided that the variance tends to inﬁnity.”
Limit theorems for the number of occupied boxes in the Bernoulli sieve (2010, background): “Starting from Karlin’s fundamental paper [19], the behaviour of Kn was studied by many authors [3, 8, 17, 20].”